ATD: Relational Point Process Models: Theory, Methods, and Applications

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Data consisting of time-stamped relational events between a set of entities (such as interactions between individuals in a community, messages between users of an online social network, or financial transactions in a stock market) have become widely available and are of great importance in disciplines as diverse as epidemiology, computer science, and finance. The literature on mathematical models for this class of problems is limited, and mostly focuses on situations where the occurrence of an event is likely to create additional ones. While this type of self- and mutually-excitatory processes are of interest in many social sciences applications, they are not appropriate in numerous other settings. This project aims to develop novel mathematical models for time-stamped relational data that allow for a wider range of behaviors, along with the computational and theoretical tools necessary to learn those models from data, and to predict the future behavior of the systems. The methods developed in this project have direct relevance to the mission of agencies such as the National Geospatial-Intelligence Agency, the National Security Agency and the Federal Bureau of Investigation, the Department of Homeland Security, and various National Laboratories. Hence, the project is likely to have a clear and direct impact on defense and natural security (DNS). Besides technical advances, this project will also contribute to the development of a workforce with strong skills in mathematical and statistical sciences, familiarity with DNS applications and awareness of the career opportunities in the public sector. Finally, the project will also assist in the dissemination of the work performed by all PIs supported by the ATD program and contribute to broader workforce development by providing logistical support to the organization of an annual ATD workshop. This project will provide support for one graduate student per year.Time-stamped relational event data is often analyzed using static or discrete time network models by aggregating events over time to generate network snapshots. However, while this kind of aggregation can be helpful in some applications such as change-point analysis, it discards a significant amount of information that can be critical to understanding the underlying micro-processes that drive the generation of the data. This project will develop a general framework for continuous time relational point process that can be used to directly model the time-stamped data, thereby avoiding the need for aggregation. In addition to presenting a general framework that can be used to design and evaluate relational point processes, this proposal develops novel instantiations of this general class of models that are suitable for various applications related to epidemiology, human mobility, information diffusion, and finance. These applications are all highly relevant to the defense and national security community in general, and the National Geospatial-Intelligence Agency in particular. Our contributions include relational versions of repulsive Matern and Markov renewal process, as well as novel constructions of relational Hawkes processes that rely on its branching Poisson cluster construction and allow for simultaneous interactions between nodes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.